Introducing HyperDiffusion: Unconditional Generative Modeling for Implicit Neural Fields

Implicit neural fields are a powerful tool in AI, as they provide a compact and high-fidelity representation of complex signals. However, applying generative modeling directly on these fields to create new data poses a challenge due to their lack of a regular grid structure. In this article, we introduce HyperDiffusion, a novel approach that tackles this issue by operating on MLP weights to generate new neural implicit fields.

Understanding the Problem

Traditionally, a multilayer perceptron (MLP) is used to encode implicit neural fields, mapping coordinates to signals. While this method has shown great promise, it doesn’t lend itself easily to generative modeling. Generating new data directly from implicit neural fields becomes tricky due to their irregular grid structure.

Introducing HyperDiffusion

HyperDiffusion is our solution to the challenge of generative modeling for implicit neural fields. Instead of working directly on the fields themselves, HyperDiffusion operates on MLP weights to generate new neural implicit fields. Here’s how it works:

First, a collection of MLPs is optimized to accurately represent individual data samples. This step ensures that our model faithfully captures the essence of the original data.

Next, we train a diffusion process within the MLP weight space. This process allows us to model the distribution of neural implicit fields that underlie the data. By doing so, HyperDiffusion enables generative modeling for these fields, providing a unified framework for synthesizing new data.

The Advantages of HyperDiffusion

HyperDiffusion offers several advantages when it comes to generative modeling of implicit neural fields:

1. Implicit and Compact Representation: HyperDiffusion works with implicit neural fields, which are known for their high-fidelity representation of complex signals. Additionally, this approach provides a compact representation that efficiently captures the essence of the data.
2. Modeling Complex Signals in 3D Shapes and 4D Mesh Animations: With HyperDiffusion, you can generate new data not only for 3D shapes but also for 4D mesh animations. This makes it a versatile tool for various applications.
3. A Unified Framework: By operating directly on MLP weights, HyperDiffusion offers a unified framework that seamlessly combines optimization and diffusion processes. This fusion of techniques allows for efficient generative modeling.